Existing Approaches of Link Budget Design
A main characteristics of any type of wireless network performance is a Link Budjet that based on average path loss evaluation according to reaction and response of the corresponding terrestrial propagation channel, rural, mixed residential, sub-urbanm and urban. Existing approaches for average path loss prediction were fully described during recent decades [1-14]. Thus, the empirical Okumura-Hata model [1, 2], Bertoni approach [3-6], Walfish-Ikegami approach [7], and 2-D stochastic approach [8-10], require signal intensity decay law versus the range r between the terminal antenna, transmitter and receiver, ofL(I)∝d−γ,γ=2.6−4.0  (1)Further, the abovementioned approaches were relevant only for specific scenarios, with accuracy of 10-15 dB relative to experimental data.
Approximate concept of link budget estimation were described, based on numerous experimental data obtained for various terrestrial communication links such as in Steele, R., Mobile Radio Communications (called the Steele's approach [11, 12]). According to this predicting concept, the expected median signal power at the moving vehicle/subscriber (MV/MS) must be derived, first of all, for determining the radio coverage of a specific base station (BS) and the interference tolerance for the purpose of cellular map construction. As suggested by Steele's approach, the total signal power at the receiver, PRX, is also subjected to slow fading or shadowing and fast fading, which are mainly caused by the characteristic terrain features in the vicinity of BS and MV. Usually, when designing the network power budget and the coverage area patter, the slow and fast fading phenomena are taken into account, introducing a shadow fading margin LSF=2σSh, where σSh is the standard deviation of shadowing, as suggested in Steele's approach and in Rappaport, T. S., Wireless Communications [13], and a fast fading margin, LFF, as functions of the range between BS and MV.
In other words, a shadow fading margin, which usually predicted to be in the range of about 1% to 2% of the slow fading lognormal PDF, and a fast fading margin, which is typically predicted to be the in the range of about 1% to 2% of the fast fading Rayleigh or Rice PDF, may be taken into account simultaneously or separately in link budget design depending on the worst-case scenario in the concrete communication channel. This situation is often referred to as “fading margin overload” resulting in a very low-level received signal almost entirely covered in noise. The probability of such worst cases determines the event of how rapidly the signal level drops below the receiver's noise floor level (NFL). The probability of such an event was predicted in Steele's approach as a sum of the individual margin overload probabilities, the slow and the fast, when the error probability is close to 0.5, since the received signal is at the NFL.
According to Steele's approach and Rappaport technique, one has a slow fading margin of LSF=2σSh=10−15 dB. There assuming the Rician fast fading PDF, as more general PDF for multipath channel prediction, with the Rician parameter K=5−10 and a fast fade margin overload probability of 1%, we can obtain a fast fading margin, using so-called the Rappaport's approach as LFF=5−7 dB.
Another, concept of how to obtain the slow and fast fade margins was proposed in Saunders, S. R., Antennas and Propagation for Wireless Communication Systems (called also the Saunders' approach [14]). According to the proposed concept, the effect of slow fading or shadowing can be described as a difference between the median path loss, as predicted by any standard propagation model. To obtain the shadow fade margin, one needs information of PDF distribution of slow fading, also defined as a Gaussian process with a zero-mean Gaussian variable LSF and with a standard deviation of shadowing σL.
Using concept described in Saunders' approach, one can also estimate the fast fade margine, LFF, using well-known Ricean PDF distribution of such parameter. We will rewrite it using a new notation as
                              P          ⁢                                          ⁢          D          ⁢                                          ⁢                      F            ⁡                          (                              L                FF                            )                                      =                                            2              ⁢                              L                FF                                                                    (                rms                )                            2                                ⁢          exp          ⁢                                    {                              -                                                      L                    FF                    2                                                                              (                      rms                      )                                        2                                                              }                        ·                          exp              ⁡                              (                                  -                  K                                )                                      ·                                          J                0                            ⁡                              (                                                                            2                      ⁢                                              L                        FF                                                              rms                                    ⁢                                      K                                                  )                                                                        (        2        )            where, as in prior researches, rms=√{square root over (2)}·σF, σF is the variance of fast fading, which can be defined as following:
                              σ          F                =                                            ∫              0              ∞                        ⁢                                                            x                  2                                ·                                  p                  ⁡                                      (                    x                    )                                                              ⁢                              ⅆ                x                                              -                                    (                                                ∫                  0                  ∞                                ⁢                                  x                  ·                                      p                    ⁡                                          (                      x                      )                                                        ·                                      ⅆ                    x                                                              )                        2                                              (                  3          ⁢          a                )            Using derivations carried out in Wireless Communication Systems, in Handbook of Engineering Electromagnetics [10], we finally get:
                              σ          F                =                                            [                              2                ·                                                      (                    rms                    )                                    2                                ·                                  ⅇ                                      -                    K                                                              ]                        ·                          [                                                                                          1                      2                                        ·                                          ⅇ                      K                                                        ⁢                                                            ∫                      0                      ∞                                        ⁢                                                                  y                        3                                            ·                                              ⅇ                                                  -                                                      y                            2                                                                                              ·                                                                        I                          0                                                ⁡                                                  (                                                      2                            ·                                                          K                                                        ·                            y                                                    )                                                                    ·                                              ⅆ                        y                                                                                            -                                                      (                                                                  ∫                        0                        ∞                                            ⁢                                                                        y                          2                                                ⁢                                                                              ⅇ                                                                                          -                                y                                                            ⁢                                                                                                                          ⁢                              2                                                                                ·                                                                                    I                              0                                                        ⁡                                                          (                                                              2                                ·                                                                  K                                                                ·                                y                                                            )                                                                                ·                                                      ⅆ                            y                                                                                                                )                                    2                                            ]                                ⁢                      1            /            2                                              (                  3          ⁢          b                )            So, as above for slow fading, we have here the loss due to fast fading, which can be expressed as:LFF=10·log10(σF)[dB]  (4)Here in (3b) the Ricean parameter K is presented as the ratio of LOS component (deterministic part of the total signal) and NLOS component (random part of the total signal), i.e.,
                    K        =                                                            L                ⁢                                                                  ⁢                O                ⁢                                                                  ⁢                S                            -              component                                                      N                ⁢                                                                  ⁢                L                ⁢                                                                  ⁢                O                ⁢                                                                  ⁢                S                            -              component                                =                                    〈                              I                co                            〉                                      〈                              I                inc                            〉                                                          (        5        )            In (5), Ico and Iincc are the coherent and incoherent parts of the total field intensity, respectively. When parameters rms and K a-priori are known, one can, by use of results presented in [10], find LFF.
According to the scenario of how to obtain the link power budget proposed in Saunders' approach [14] one has two variants of link-budget design prediction. The first variant describes Estimation of the slow fade margin, z, deriving the median path loss, L, by using well-known propagation models, and using the maximum acceptable path loss, Lm, as well as the range between concrete terminal antennas, the knowledge of which is done for the performed wireless system. Estimation of fast fade margin can be done, if the standard deviation and the Ricean parameter K are known for the concrete propagation channel and wireless system. The second variant describes estimation of the slow fade margin, z, and the range between concrete terminal antennas using derivation of the median path loss, L, through well-known propagation models, and using the standard deviation of slow fading, σL, as well as the percentage of the success communication for the concrete wireless system performed.
As for the fast fade margin, LFF, it can be obtained if the standard deviation of fast fading, σ, or rms, as well as the probability of the successful communication are known for the concrete wireless system. These approaches are not precise and require a great amount of measurements and statistical analysis.
Existing Approaches for Cellular Maps Design
To arrange the effective splitting of tested built-up area at cells, the designers need strict information about the law of signal power decay for the concrete situation in the site of service, i.e., need strict link budget analysis of propagation situation within each communication channel, as well as full radio coverage of each subscriber located LOS or NLOS conditions in areas of service, giving exact clearance between subscribers within each cell. Based on precise knowledge of propagation phenomena inside the cellular communication channels, it is easy to optimize cellular characteristics, such as radius of cell, reuse factor Q, channel interference parameter C/I, etc [12-14].
Standard Definition of Radius of Cell. As follows from prior researches [15-25], a better clearance between the base station (BS) and moving subscribers (MS) in clutter conditions may be reached only for LOS conditions (or direct visibility) between them. In this case, as follows from the two-ray model and the waveguide street model (see above), the cell size, Rcell, cannot be larger than the break point range, rB, at which the decay of the signal is changed from γ=2 (as in free space propagation) to γ=4 (propagation above flat terrain). If so, the law of signal decay between BS and each MS in the cell of radius Rcell≦rB is Rcell−2. Generally speaking, beyond the break point the law of signal decays versus the range between terminal antennas, describing by path-loss slope parameter γ, depends on the concrete situation in the urban scene and may be proportional to R−γ with γ>2 (γ=4−6, see standard propagation models presented above).
As follows from other models in rural and mixed residential areas with a rare buildings' distribution the path-loss slope parameter γ describing the received signal decay is changed from γ=2.5 to γ=4.0, which in a good agreement with existing propagation models (see above). In other words, in such areas field attenuation is faster than that in LOS conditions of free space.
Co-channel Interference Parameter Definition. Using standard methods of C/I evaluation, one can easy estimate this ratio based on the classical formula:
                              C          I                =                  10          ⁢                      log            ⁡                          [                                                1                  6                                ⁢                                  (                                                            D                      γ                                                              R                      cell                      γ                                                        )                                            ]                                                          (        6        )            where, according to strategy of cellular pattern design described in [10-14], D is the reuse distance between co-interferer cells operated with the same frequency bands and γ is a factor of signal strength attenuation inside and outside the cell, as is illustrated by these figures.Existing Methods of Channel (Frequency) Assignment
Let us briefly introduce a well-known heuristic approach on how to obtain C/I-ratio based on mathematical models by accounting the Walfisch-Ikegami model (WIM) [7, 10] of signal power decay in urban environment.
The frequency assignment problem, was represented in the form of the heuristic algorithm developed in [15-17] based on cell configuration, which does not follow the classical hexagonal-cell homogeneous concept with a periodic frequency reuse pattern. This algorithm is based on the binary constraints between pair if transmitters presented in the following form:|fi−fj|>k,k≧0  (7)where fi and fj are the frequencies assigned to transmitters i and j, respectively. Different configurations of the cellular pattern were analyzed for channel (frequency) assignment purposes with applications to real non-regular non-uniform radio networks, mobile and stationary, considering:                cellular maps with different dimensions of cells,        cellular maps with irregular shapes of cells,        cellular maps with certain level of intercell overlapping. For such configurations of cells we need, instead of classical formulation of carrier to interference ratio (C/I) for various γ, to use the following formula [10-14]:        
                                          (                          C              I                        )                    i                =                              R            i                          -              4                                                          ∑                              j                ∈                                  M                  i                                                                                                  ⁢                          d              ij                              -                4                                                                        (        8        )            Here, we take a simple two-ray propagation model (called also the “flat terrain” model) with γ=4. Notice that all notations are changed here from those used in to be unified with those used in this patent presentation. Here Ri is a radius of cell i; Mi is the set of all the cells (excluding cell i) which use the same bandwidths (channels) as cell i; dij is the worst case distance between interfering cell j and cell i. The latter can be found asdij=√{square root over ((xi−xj)2+(yi−yj)2)}−Ri  (9)where (xi,yi) and (xj,yj) are the Cartesian coordinates of base stations (BSs) of cells i and j, respectively. Using this simplest propagation model, in the co-channel interference constraint was obtained for C/I threshold α=1/β=18 dB [18-25]:
                                          ∑                          j              ∈                              M                i                                                                                    ⁢                                    d              ij                              -                4                                                    R              i                              -                4                                                    ≤        β                            (        10        )            Sufficient improvements of model were obtained by introducing adjacent channel interference adj_factork=−a(1+log2 k), where k is the bandwidth separation (in number of channels) between the adjacent channel frequency and central frequency of the corresponding filter. Typical value for a is 18 dB (as α=18 dB in [21]), and for k=1 an adjacent channel is attenuated by a factor equal to 0.015 [22-25].Existing Methods of Grade-of-Service (GoS) Performance
The fixed (FWA) or mobile (MWA) wireless access systems, unlike the wire-line systems, may have degraded quality of service (QoS) due to low link reliability caused by propagation characteristics (such as shadowing, multipath or multi-carrier interference and sensitivity of receivers) and by degradation of grade of service (GOS), due to high service demand and a low number of call resources. The most elementary stage of a system deployment is the link budget design, which is the main parameter of wireless communication links. It is based on propagation characteristics of the channel and describes signal power distribution along the radio path between the base-station antenna and terminal. The link budget is a balance sheet of gains and losses. As was mentioned above, by calculating the link budget, we evaluate the link performance.
The fixed (FWA) or mobile (MWA) wireless access systems, unlike the wire-line systems, may have degraded quality of service (QoS) due to low link reliability caused by propagation characteristics (such as shadowing, multipath or multi-carrier interference and sensitivity of receivers) and by degradation of grade of service (GOS), due to high service demand and a low number of call resources.
As for the GOS, a classical GOS analysis for circuit-switched (voice) traffic uses the Erlang-B or Erlang-C formulas, which is a special case of the birth and death (B&D) equation for calculating the total system capacity and the probability of working without call congestion [26-28]. Other models are used for other types of traffic, however most used in the literature classical approach is based on these formulas. So, we will focus on the Erlang B model. This, finally, the estimated total grade of service (GoS), which is the probability that a user tries to initiate a call and the call is either blocked or drops is calculated by both of those procedures together. However, Erlang-B formula is justified only in cases where all users have access to all resources of the system (a situation of full-availability). In wireless systems, due to propagation limitations, such as obstacles and wave attenuation, one user has limited access to the system resources. This is referred to as limited-availability and, thus, we cannot use the classical approach of using Erlang-B formula according to [26-29].
Moreover, in FWA systems, one user gets service from one cell. The user is part of a user group that is covered by one or more cells. If one user has optional access to more than one cell, the system has to allocate the user to one of these cells in order to achieve an optimal grade-of-service; this refers to load-balancing. The decision rule of user allocation refers to the load-balancing algorithm.
Therefore, to cover existing limitations, we propose below a new approach and methodology, as an extension of the existing classical approach mentioned above. As in other sections above, in our novel stochastic multi-parametric approach we take into account two types of areas, following [30-34]: mixed residential area having low buildings with trees and vegetation and urban area containing mostly high buildings in a dense built-up area.
Existing Approaches of Quality of Service (QOS) Performance
QoS is defined by characteristics called the capacity, as a maximum rate of data stream via the communication channel. The capacity of a communication channel is defined as the traffic load of data in bits per second. It is accepted to use Shannon-Hartley formula, in order to calculate the capacity of the channel [26-28]:C=Bw log2[1+SNR]  (11)where SNR is the signal-to-noise ratio for the channel with the additive white Gaussian noise (AWGN). Here, we will define SNR as a measure of the signal strength relative to the noise. The ratio is usually measured in dB.
                              S          ⁢                                          ⁢          N          ⁢                                          ⁢          R                =                              10            ⁢                          log              ⁡                              (                                                      P                    R                                                        N                    R                                                  )                                              =                                    P                              R                ⁡                                  [                  dB                  ]                                                      -                          N                              R                ⁡                                  [                  dB                  ]                                                                                        (        12        )            The classical approach is usually used to estimate the data capacity of the communication link using (11)-(12). According to its definition, the capacity of an AWGN channel of bandwidth Bw, wherein the signal to noise ratio is ρ, is given by:C=Bw log2[1+ρ]  (13)and the spectral efficiency is given by:
                              C          ~                =                              C                          B              w                                =                                    log              2                        ⁡                          [                              1                +                ρ                            ]                                                          (        14        )            In the first approach only the Gaussian noise (called additive) density N0 inside the channel with a large bandwidth Bw of noise spectrum is taken into account, i.e.,
                    C        =                              B            w                    ⁢                                    log              2                        ⁡                          [                              1                +                                  S                                                            N                      0                                        ⁢                                          B                      w                                                                                  ]                                                          (        15        )            Here C is the channel capacity in bits per second, Bw is the one-way transmission bandwidth of the channel in Hz, S is the signal power in W=J/s, and N0 is the single-sided additive (white) noise power spectral density also in W/Hz, that is, Nadd=N0Bw. Practical channels are compared to the ideal channel by selecting detection error probability of 10−6 and finding the SNR necessary to achieve it. Another criterion of efficiency of the communication channel can be defined by use other data stream parameter such as the bit error rate (BER). The BER usually is achieved at a practical communication system. For example, for an encoded BPSK system, the BER is given by:BER(ρ)=Q(√{square root over (2ρ)})  (16)Here Q(·) is the tabulated classical Gaussian function. For BER in the percentage of bits that have errors relative to the total number of bits received in a transmission another formula can be used [29]:
                              B          ⁢                                          ⁢          E          ⁢                                          ⁢          R                =                              1            2                    ⁢                                    ∫              0              ∞                        ⁢                                          p                ⁡                                  (                  x                  )                                            ⁢                              erfc                (                                                                            S                      ⁢                                                                                          ⁢                      N                      ⁢                                                                                          ⁢                      R                                                              2                      ⁢                                              2                                                                              ⁢                  x                                )                            ⁢                              ⅆ                x                                                                        (        17        )            where p(x) is the probability density function and erfc(·) is the well-known error function [13, 26-29].
Using these parameters, each designer of wireless networks can easily predict data stream parameters within each communication link with AWGN. Effects of interference can be regarded as another source of effective noise, which raises the noise level for calculating the error rates. In this case we must introduce in (8.4) together with Nadd also the noise caused by interference Nint.
As was shown by Rappaport [13], each Gaussian-like noise can be additively taken into account in the denominator of formula (11). Thus for K-carrier system each carrier/subscriber of number i can affect the desired subscriber as an additional interferer which can be described by a Gaussian-like noise. Then, according to Rappaport, we can write:
                    C        =                              B            w                    ⁢                                    log              2                        [                          1              +                              S                                                                            N                      0                                        ⁢                                          B                      w                                                        +                                                            ∑                                              i                        =                        1                                                                    K                        -                        1                                                              ⁢                                          N                      i                                                                                            ]                                              (        18        )            where Ni is the power of i-subscriber which affects as a additive white noise for the desired subscriber.